给定一个无限长的二叉树，其模式如下：
1
/ \
2 3
/ \ / \
4 5 6 7
/ \ / \ / \ / \
......................
还给出了大小为N且数字为K的数组arr 。任务是依次用颜色i(1 <= i <= N)为节点arr [i]的所有子树着色。给所有子树着色后，找到节点K的颜色。
注意：-最初，所有节点的颜色均为0。
Input :arr[] = {3, 2, 1, 3}, K = 7
Output : 4
Explanation :
After applying the color 1 to subtree at node 3, node 7 contains color 1.
After applying the color 2 to subtree at node 2, node 7 contains color 1.
After applying the color 3 to subtree at node 1, node 7 contains color 3.
After applying the color 4 to subtree at node 3, node 7 contains color 4.
Input : arr[] = {3, 2, 1, 3}, K = 4
Output : 3
Explanation :
After applying the color 1 to subtree at node 3, node 4 contains color 0.
After applying the color 2 to subtree at node 2, node 4 contains color 2.
After applying the color 3 to subtree at node 1, node 4 contains color 3.
After applying the color 4 to subtree at node 3, node 4 contains color 3.
天真的方法是为每个索引i(1 <= i <= N)更新子树中所有节点的颜色，直到节点的级别小于给定节点K的级别。在N次操作之后，将打印节点K的颜色。
一种有效的方法是使用哈希
- 首先，将所有具有各自颜色的节点插入地图中(以防万一，如果一个节点有多种颜色，则保留最大颜色数)。
- 查找给定节点k的所有祖先，并输出具有最大数量的颜色。 (如果当前节点是x ，那么(x-1)/ 2或x / 2是其祖先)
下面是上述方法的实现：
CPP
// CPP program to find color of the node
#include
using namespace std;
// Function to find color of the node
int findColor(map mapWithColor, int query)
{
// Maximum is to store maximum color
int maximum = 0;
// Loop to check all the parent
// values to get maximum color
while (query >= 1) {
// Find the number into map and get maximum color
if (mapWithColor.find(query) != mapWithColor.end())
{
// Take the maximum color and
// assign into maximum variable
maximum = max(maximum, mapWithColor[query]);
}
// Find parent index
if (query % 2 == 1)
query = (query - 1) / 2;
else
query = query / 2;
}
// Return maximum color
return maximum;
}
// Function to build hash map with color
map buildMapWithColor(int arr[], int n)
{
// To store color of each node
map mapWithColor;
// For each number add a color number
for (int i = 0; i < n; i++) {
// Assigning color
mapWithColor[arr[i]] = i + 1;
}
// Return hash map
return mapWithColor;
}
// Driver code
int main()
{
int arr[] = { 3, 2, 1, 3 };
int n = sizeof(arr) / sizeof(arr[0]);
int k = 7;
// Build mapWithColor
map mapWithColor = buildMapWithColor(arr, n);
// Print the maximum color
cout << findColor(mapWithColor, k);
return 0;
} Java
// JAVA program to find color of the node
import java.util.*;
class GFG
{
// Function to find color of the node
static int findColor(HashMap mapWithColor, int query)
{
// Maximum is to store maximum color
int maximum = 0;
// Loop to check all the parent
// values to get maximum color
while (query >= 1)
{
// Find the number into map and get maximum color
if (mapWithColor.containsKey(query))
{
// Take the maximum color and
// assign into maximum variable
maximum = Math.max(maximum, mapWithColor.get(query));
}
// Find parent index
if (query % 2 == 1)
query = (query - 1) / 2;
else
query = query / 2;
}
// Return maximum color
return maximum;
}
// Function to build hash map with color
static HashMap buildMapWithColor(int arr[], int n)
{
// To store color of each node
HashMap mapWithColor = new HashMap();
// For each number add a color number
for (int i = 0; i < n; i++)
{
// Assigning color
mapWithColor.put(arr[i], i + 1);
}
// Return hash map
return mapWithColor;
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 3, 2, 1, 3 };
int n = arr.length;
int k = 7;
// Build mapWithColor
HashMap mapWithColor = buildMapWithColor(arr, n);
// Print the maximum color
System.out.print(findColor(mapWithColor, k));
}
}
// This code is contributed by PrinciRaj1992 Python3
# Python3 code program to find color of the node
# Function to find color of the node
def findColor(mapWithColor, query):
# Maximum is to store maximum color
maximum = 0
# Loop to check all the parent
# values to get maximum color
while (query >= 1):
# Find the number into map and get maximum color
if (query) in mapWithColor.keys():
# Take the maximum color and
# assign into maximum variable
maximum = max(maximum, mapWithColor[query])
# Find parent index
if (query % 2 == 1):
query = (query - 1) // 2
else:
query = query // 2
# Return maximum color
return maximum
# Function to build hash map with color
def buildMapWithColor(arr, n):
# To store color of each node
mapWithColor={}
# For each number add a color number
for i in range(n):
# Assigning color
mapWithColor[arr[i]] = i + 1
# Return hash map
return mapWithColor
# Driver code
arr = [3, 2, 1, 3]
n = len(arr)
k = 7
# Build mapWithColor
mapWithColor = buildMapWithColor(arr, n)
# Print the maximum color
print(findColor(mapWithColor, k))
# This code is contributed by mohit kumar 29C#
// C# program to find color of the node
using System;
using System.Collections.Generic;
class GFG
{
// Function to find color of the node
static int findColor(Dictionary mapWithColor, int query)
{
// Maximum is to store maximum color
int maximum = 0;
// Loop to check all the parent
// values to get maximum color
while (query >= 1)
{
// Find the number into map and get maximum color
if (mapWithColor.ContainsKey(query))
{
// Take the maximum color and
// assign into maximum variable
maximum = Math.Max(maximum, mapWithColor[query]);
}
// Find parent index
if (query % 2 == 1)
query = (query - 1) / 2;
else
query = query / 2;
}
// Return maximum color
return maximum;
}
// Function to build hash map with color
static Dictionary buildMapWithColor(int []arr, int n)
{
// To store color of each node
Dictionary mapWithColor = new Dictionary();
// For each number add a color number
for (int i = 0; i < n; i++)
{
// Assigning color
if(mapWithColor.ContainsKey(arr[i]))
mapWithColor[arr[i]] = i + 1;
else
mapWithColor.Add(arr[i], i + 1);
}
// Return hash map
return mapWithColor;
}
// Driver code
public static void Main(String[] args)
{
int []arr = { 3, 2, 1, 3 };
int n = arr.Length;
int k = 7;
// Build mapWithColor
Dictionary mapWithColor = buildMapWithColor(arr, n);
// Print the maximum color
Console.Write(findColor(mapWithColor, k));
}
}
// This code is contributed by Rajput-Ji 输出：
4